Phase extraction from interferograms with unknown tilt phase shifts based on a regularized optical flow method

A novel method is presented to extract phase distribution from phase-shifted interferograms with unknown tilt phase shifts. The proposed method can estimate the tilt phase shift between two temporal phase-shifted interferograms with high accuracy, by extending the regularized optical flow method with the spatial image processing and frequency estimation technology. With all the estimated tilt phase shifts, the phase component encoded in the interferograms can be extracted by the least-squares method. Both simulation and experimental results have fully proved the feasibility of the proposed method. Particularly, a flat-based diffractive optical element with quasi-continuous surface is tested by the proposed method with introduction of considerably large tilt phase shift amounts (i.e., the highest estimated tilt phase shift amount between two consecutive frame reaches 6.18λ). The phase extraction result is in good agreement with that of Zygo's MetroPro software under steady-state testing conditions, and the residual difference between them is discussed. In comparison with the previous methods, the proposed method not only has relatively little restrictions on the amounts or orientations of the tilt phase shifts, but also works well with interferograms including open and closed fringes in any combination.